{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compact Telescope"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from optiland import optic, physical_apertures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize an optic system\n",
    "system = optic.Optic()\n",
    "\n",
    "# define physical aperture of first mirror\n",
    "aperture1 = physical_apertures.RadialAperture(r_min=1.7, r_max=4.2)\n",
    "\n",
    "# define physical aperture of third mirror\n",
    "aperture3 = physical_apertures.RadialAperture(r_min=0.65, r_max=1.7)\n",
    "\n",
    "# add surfaces to the system\n",
    "system.add_surface(index=0, thickness=np.inf)\n",
    "system.add_surface(\n",
    "    index=1,\n",
    "    thickness=-5.5119,\n",
    "    radius=-16.4794,\n",
    "    material=\"mirror\",\n",
    "    conic=-0.9774823,\n",
    "    aperture=aperture1,\n",
    ")\n",
    "system.add_surface(\n",
    "    index=2,\n",
    "    thickness=5.9056,\n",
    "    radius=np.inf,\n",
    "    material=\"mirror\",\n",
    "    is_stop=True,\n",
    ")\n",
    "system.add_surface(\n",
    "    index=3,\n",
    "    thickness=-5.9056,\n",
    "    radius=-5.2556,\n",
    "    material=\"mirror\",\n",
    "    conic=-0.4605796,\n",
    "    aperture=aperture3,\n",
    ")\n",
    "system.add_surface(index=4, thickness=9.2807, radius=np.inf, material=\"mirror\")\n",
    "system.add_surface(index=5)\n",
    "\n",
    "# add aperture\n",
    "system.set_aperture(aperture_type=\"imageFNO\", value=5.0)\n",
    "\n",
    "# add field\n",
    "system.set_field_type(field_type=\"angle\")\n",
    "system.add_field(y=0)\n",
    "system.add_field(y=0.5)\n",
    "\n",
    "# add wavelength\n",
    "system.add_wavelength(value=0.587, is_primary=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+----+---------------+----------+-------------+------------+-----------+-----------------+\n",
      "|    | Type          |   Radius |   Thickness | Material   |     Conic |   Semi-aperture |\n",
      "|----+---------------+----------+-------------+------------+-----------+-----------------|\n",
      "|  0 | Planar        | inf      |    inf      | Air        |  0        |        4.08208  |\n",
      "|  1 | Standard      | -16.4794 |     -5.5119 | Mirror     | -0.977482 |        4.08208  |\n",
      "|  2 | Stop - Planar | inf      |      5.9056 | Mirror     |  0        |        1.30329  |\n",
      "|  3 | Standard      |  -5.2556 |     -5.9056 | Mirror     | -0.46058  |        1.67397  |\n",
      "|  4 | Planar        | inf      |      9.2807 | Mirror     |  0        |        0.966242 |\n",
      "|  5 | Planar        | inf      |    nan      | Air        |  0        |        0.344003 |\n",
      "+----+---------------+----------+-------------+------------+-----------+-----------------+\n"
     ]
    }
   ],
   "source": [
    "system.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "system.draw(num_rays=2)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
